Ask a New Question
Menu

Which option is true about the outliers of the skewed dataset 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16?(1 point)

Responses

There are no outliers in the dataset.
There are no outliers in the dataset.

The outliers of the dataset are 5, 14, and 16.
The outliers of the dataset are 5, 14, and 16.

The outliers of the dataset are 14 and 16.
The outliers of the dataset are 14 and 16.

The only outlier of the dataset is 16.

1 answer

To determine the outliers in the skewed dataset (5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16), we can use the Interquartile Range (IQR) method.

  1. Find the Quartiles:

    • Arrange the dataset in ascending order: 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16.
    • Q1 (First Quartile) is the median of the first half (first 6 numbers): 6.5 (between 6 and 7).
    • Q3 (Third Quartile) is the median of the second half (last 6 numbers): 9.5 (between 9 and 14).

  2. Calculate the IQR:

    • IQR = Q3 - Q1 = 9.5 - 6.5 = 3.

  3. Calculate the lower and upper bounds for outliers:

    • Lower Bound = Q1 - 1.5 * IQR = 6.5 - 1.5 * 3 = 6.5 - 4.5 = 2.
    • Upper Bound = Q3 + 1.5 * IQR = 9.5 + 1.5 * 3 = 9.5 + 4.5 = 14.

  4. Determine outliers:

    • Any values below 2 or above 14 are outliers.
    • In the dataset, the numbers below 2 are none, and the numbers above 14 are 16 (since 14 is the upper bound).

Based on this analysis, the outliers in the dataset are only 16.

Therefore, the correct response is:

The only outlier of the dataset is 16.